Fulfill the following conditions to unlock different structure decks in the game.

Deck	Condition
Curse of Darkness	Duel Gordon in Chapter II.
Dinosaur's Rage	Start Chapter II.
Dragunity Legion	Start Chapter VI.
Fury From The Deep	Play in the Rental Deck Tournament in Chapter I.
Invincible Fortress	Play in the Rental Deck Tournament in Chapter I.
Lord of the Storm	Start Chapter II.
Lost Sanctuary	Start Chapter VI.
Machina Mayhem	Start Chapter V.
Machine Re-Volt	Start Chapter II.
Rise of the Dragon Lords	Start Chapter III.
Spellcaster's Command	Start Chapter V.
Spellcaster's Judgment	Play in the Rental Deck Tournament in Chapter I.
Surge of Radiance	Duel Gordon in Chapter II.
The Dark Emperor	Start Chapter III.
Warrior's Strike	Start Chapter IV.
Warrior's Triumph	Play in the Rental Deck Tournament in Chapter I.
Zombie World	Start Chapter IV.